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- Projective_space abstract "In mathematics, a projective space is the set of lines through the origin of a vector space V. The cases when V = R2 and V = R3 are the projective line and the projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.The idea of a projective space relates to perspective, more precisely to the way an eye or a camera projects a 3D scene to a 2D image. All points which lie on a projection line (i.e., a "line-of-sight"), intersecting with the entrance pupil of the camera, are projected onto a common image point. In this case the vector space is R3 with the camera entrance pupil at the origin and the projective space corresponds to the image points.Projective spaces can be studied as a separate field in mathematics, but are also used in various applied fields, geometry in particular. Geometric objects, such as points, lines, or planes, can be given a representation as elements in projective spaces based on homogeneous coordinates. As a result, various relations between these objects can be described in a simpler way than is possible without homogeneous coordinates. Furthermore, various statements in geometry can be made more consistent and without exceptions. For example, in the standard geometry for the plane, two lines always intersect at a point except when the lines are parallel. In a projective representation of lines and points, however, such an intersection point exists even for parallel lines, and it can be computed in the same way as other intersection points.Other mathematical fields where projective spaces play a significant role are topology, the theory of Lie groups and algebraic groups, and their representation theories.".
- Projective_space thumbnail Railroad-Tracks-Perspective.jpg?width=300.
- Projective_space wikiPageExternalLink ProjectiveSpace.html.
- Projective_space wikiPageExternalLink planes.
- Projective_space wikiPageID "242135".
- Projective_space wikiPageRevisionID "604280613".
- Projective_space first "V.V.".
- Projective_space hasPhotoCollection Projective_space.
- Projective_space id "P/p075350".
- Projective_space last "Afanas'ev".
- Projective_space title "Projective Space".
- Projective_space title "projective space".
- Projective_space urlname "ProjectiveSpace".
- Projective_space subject Category:Projective_geometry.
- Projective_space comment "In mathematics, a projective space is the set of lines through the origin of a vector space V. The cases when V = R2 and V = R3 are the projective line and the projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.The idea of a projective space relates to perspective, more precisely to the way an eye or a camera projects a 3D scene to a 2D image.".
- Projective_space label "Espace projectif".
- Projective_space label "Espacio proyectivo".
- Projective_space label "Espaço projetivo".
- Projective_space label "Projectieve ruimte".
- Projective_space label "Projective space".
- Projective_space label "Projektiver Raum".
- Projective_space label "Przestrzeń rzutowa".
- Projective_space label "Spazio proiettivo".
- Projective_space label "Проективное пространство".
- Projective_space label "فضاء إسقاطي".
- Projective_space label "射影空間".
- Projective_space sameAs Projektivní_prostor.
- Projective_space sameAs Projektiver_Raum.
- Projective_space sameAs Προβολικός_χώρος.
- Projective_space sameAs Espacio_proyectivo.
- Projective_space sameAs Espace_projectif.
- Projective_space sameAs Spazio_proiettivo.
- Projective_space sameAs 射影空間.
- Projective_space sameAs 사영공간.
- Projective_space sameAs Projectieve_ruimte.
- Projective_space sameAs Przestrzeń_rzutowa.
- Projective_space sameAs Espaço_projetivo.
- Projective_space sameAs m.01k44_.
- Projective_space sameAs Q877775.
- Projective_space sameAs Q877775.
- Projective_space wasDerivedFrom Projective_space?oldid=604280613.
- Projective_space depiction Railroad-Tracks-Perspective.jpg.
- Projective_space isPrimaryTopicOf Projective_space.
